If f(x)= | array ccc 1 & 6+x & 36+x^2 0 & x-3 & 3 x^2-27 0 & 2 x-4 & 8 x^2-32 array | , then _ x 1 f(x) f(-x) =

Step-by-step solution

aligned & f( x )= | array ccc 1 & 6+x & 36+x^2 0 & x-3 & 3 x^2-27 0 & 2 x-4 & 8 x^2-32 array | & =1 [(x-3) (8 x^2-32 )-(2 x-4) (3 x^2-27 ) ]+0 & =8 x^3-32 x-24 x^2+96- (6 x^3-54 x-12 x^2+108 ) & f(x)=2 x^3-12 x^2+22 x-12=2(x-1)(x-2)(x-3) & Now, f(-x)=-2(x+1)(x+2)(x+3) & _ x 1 f(x) f(-x) = _ x 1 2(x-1)(x-2)(x-3) -2(x+1)(x+2)(x+3) =0 aligned